Presentazione orale al convegno TMS 2010 - 139th Annual Meeting & Exhibition, svoltosi a Seattle (USA) dal 14/02/2010 al 18/02/201

Firrao D.

MATTEIS, PAOLO

RUSSO SPENA, PASQUALE

English

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEOn plastic notch effects in quenched and tempered steels / Russo Spena P.; Firrao D.; Matteis P.. - (2010).OriginalOn plastic notch effects in quenched and tempered steelsPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2458378 since:P. Russo Spena1, D. Firrao2, P. Matteis2 1Politecnico di Torino, Dipartimento di Sistemi di Produzione ed Economia dell’Azienda 2Politecnico di Torino, Dipartimento di Scienza dei Materiali ed Ingegneria Chimica TMS 2010 – February 14-18, 2010  - Seattle, WA, USA Prof.  Donato  Firrao ON PLASTIC NOTCH EFFECTS IN QUENCHED AND TEMPERED STEELS Introduction In 1971, Firrao and Spretnak compared the elastic-plastic Stress Concentration Factor (SCF) at fracture, kpf, with the elastic SCF, ke, and the tempering temperature , T, of  Q&T steel sheet tensile samples with variable notch tip radius. Finite Element calculations now allows to review their test results by overcoming the simplifying assumptions originally used to estimate ke and kpf . 1971 2009 Specimen preparation (I)  C Mn Cr Ni Mo Cu P S 0.37 0.7 0.85 1.91 0.23 0.10 0.013 0.007 • The AISI 4340 (% wt.) steel was cold-rolled to 1.78 mm sheet and annealed   • 1.14 mm thick, smooth or notched tensile samples, were machined from the sheet • The notches were machined by EDM with tip diameters, φ, from 0.13 to 3.17 mm φ [mm] • The samples were austenitized at 843 C for 30 min and quenched • This was done in salt baths and inside clamps, with steps at 704 C for 20 min during heating and at 204 C for 5 min during quenching, to minimize deformations and surface alterations  • The samples were then reheated at 177 C for 1 h, tempered at T = 316 C for 2.5 h, or T = 371, 427, 510 or 593 C for 2 h, and cooled in air • 5 smooth samples and 27 notched samples with different notch diameters were tested for each tempering temperature – total: 160 samples Specimen preparation (II)  Smooth tensile test results • The fracture always occurred on a surface inclined of ~35  from the tensile axis • Necking did not contribute significantly to the elongation at fracture (El.) • The strain was recorded with extensometers up to ε ≈ 0.016 T HRC UTS El. C - MPa % 316 49 1560 4.6 371 46 1425 5.3 427 43 1327 5.2 510 39 1129 6.7 593 35 1120 4.5 Finite Elements models of notched samples 3D models:  - 1/8 of the sample central region modeled with tetrahedral elements - 9 meshes with notch diameters φ from 0.125 to 3.18 mm - Elements size 20 - 50 µm around the notch (varying with φ), up to 1 mm elsewhere - 70,000 to 160,000 degrees of freedom (varying with φ)  Boundary conditions: - Remote stress and symmetry planes - Engineering stress σ defined in respect to the minimum undeformed cross section  Elastic or  Elastic–Plastic material model: - E = 200 GPa and υ = 0.33 - Von Mises yielding criterion, associated plastic flow law, isotropic hardening - Plastic flow stress vs. equivalent plastic strain curves obtained from the smooth tensile tests, for each T, extrapolated up to 0.1 – 0.6 eq. plastic strain   Elastic-plastic loading: -75 MPa σ steps, up to above the largest experimental fracture stress (σf), for each T  Fracture NOT modeled         -       45 independent FE calculations Stress Concentration Factors (I) Firrao and Spretnak estimated ke by using the Dixon plane stress formula, where a is the notch half-width (5.08 mm) and W is the sample width (25.4 mm): This is compared with the SCF calculated by FE at surface (Sur.) or mid-plane (Cen.), in the elastic (El.) case or in selected Elastic-Plastic  (El.-Pl.) ones: Triaxiality ratios  Notch tip triaxiality ratio in the 3D elastic cases -  would be 0 for plane stress and υ = 0.33 for plane strain Notch diam., φ, mm Distance from the sample mid-plane, mm • The elastic stress state goes from plane stress to plane strain by decreasing φ • During the elastic-plastic loading, the triaxiality ratio evolves in a complex manner, with values even higher than ν in some instances. Center-plane elastic-plastic SCF, k = σyy / σ, vs. applied nominal stress, σ Stress concentration factors (II) 0.125 3.18 0.125 3.18 0.125 3.18 0.125 3.18 φ φ φ φ Calculation of ke and kpf 1971: ke from φ by the Dixon formula, kpf  = UTS / σf  2009: interpolated from FE results; ke in respect to φ, kpf  in respect to φ and σf T = 593 C, center-plane ke kpf Exp. σf φ = 0.125 φ = 3.18 Exp. φ σf : experimental notch fracture stress φ: experimental (initial) notch diameter UTS : Ultimate Tensile Stress of smooth samples Kpf  vs. Ke Experimental results elaborated on the basis of either the original method (left), or the present FE calculations (right). T T 2009 method 1971 method Conclusions 1. The notch tip stress state is close to plane stress for the smaller elastic stress concentration factors (larger notch radii), and to plane strain in the opposite case, even if the thickness is constant, due to the variation of the notch radius to thickness ratio.  2. The elastic-plastic stress concentration factor at fracture, kpf, is much larger than 1 (up to 4.5) and the first principal stress at the notch tip at fracture is much larger than the UTS.  3. The steel tempered at different temperatures exhibit much different behaviors; in particular, the notch sensitivity decreases sharply by increasing the tempering temperature from 371 to 510 C.  4. The conclusions 2) and 3) above are affected by the uncertainty due to the extrapolation of the experimental stress – strain curves. P. Russo Spena1, D. Firrao2, P. Matteis2 1Politecnico di Torino, Dipartimento di Sistemi di Produzione ed Economia dell’Azienda 2Politecnico di Torino, Dipartimento di Scienza dei Materiali ed Ingegneria Chimica TMS 2010 – February 14-18, 2010  - Seattle, WA ON PLASTIC NOTCH EFFECTS IN QUENCHED AND TEMPERED STEELS Thank yuo for your attention 

On plastic notch effects in quenched and tempered steels

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On plastic notch effects in quenched and tempered steels

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